No. Google has a large market share of search because it got in early, presented some synergistic products, heavily biased search results towards its own products to reinforce that, heavily gamed advertising bidding in its favor, placed anti-competitive requirements on hardware manufacturers of Android devices, and locked-in consumers' data so that competitors couldn't access it until it was forced by governments to allow consumers to download a copy.
Google, and Alphabet, do not today offer good products. I can go on for hours describing many years-long problems with the product offerings; culminating in my complete non-use of Google as a search engine because its results are so poor, stopped using Google News because of its tracking and curation biases, stopped using Google Mail because of its inability to provide filters that automatically mark emails as spam, stopped using Google Drive because it actively prevents many features from working in Firefox, and ... well the list can go on but I have better things to do.
"got in early" compared to what?
There were dozens of search engines before Google.
It's not that Google should be punished. It's that they should be stopped from using one product line to prop up another.
This is exactly what antitrust law should not punish. Google has a large market share of search because it offers a good product. Antitrust law should preserve competition without punishing success.
People are free to use alternatives, including Bing. If they don't, that doesn't make Google a monopoly (which indeed in search they are not). It makes Google successful! (Though it is a successful firm which does occasionally violate antitrust laws in other areas and should be punished for that.)